Question

In the given figure, if TP and TQ are tangents to a circle with centre O, so

that ∠POQ = 110°, then ∠PTQ is​

Answer 1

Answer:

70°

Step-by-step explanation:

This is the answer.

As

Central Angle =110°

<PTQ = 180-110

= 70°

Answer 2

PTQ = 70°

Step-by-step explanation:

since  TP and TQ  are the tangents to a circle with the centre O

it is given that $\angle POQ= 110$°

therefore

OP⊥PT and  OQ⊥QT

then,

$\angle OPT= 90$° and $\angle OQT = 90$°

in the quadrilateral TPOQ we have,

$\angle PTQ+ \angle TPO+\angle POQ+\angle OQT= 360$°...(sum of all the angles of the quadrilaterals is 360°)

$\angle PTQ + 90 + 110+ 90 = 360$°

$\angle PTQ + 290= 360$°

$\angle PTQ$= 360°-290° = 70°

$\angle PTQ$= 70°

hence, the value of $\angle PTQ$ is 70°

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